Estimating second order characteristics of point processes with known independent noise

The analysis of point patterns often begins with a test of complete spatial randomness using summaries such as the emptyspace function F or the nearest neighbour distance distribution function G. These functions constitute basic summaries upon which many studies are based, depending on their shape. As the map of points is usually considered accurate, Monte Carlo tests are performed on the observed pattern without taking into account position errors. However, position errors usually occur during the mapping process. The aim of this article is to quantify the impact of measurement error on descriptive distance statistics and to integrate these errors in the non-parametric analysis. An application to tropical forest species is presented.